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- W3008686246 abstract "The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - Delta u + V(x) u + g(x, u) = 0 , , quad x in T^d , , quad g (x,u) = a(x) u^3 + O(u^4 ) , $$ in any space dimension and with a multiplicative potential. The proof is based on a Nash-Moser implicit function scheme. A key step is the construction of an approximate right inverse of the linearized operators obtained at any step of the iteration. In order to avoid the difficulty posed by the violation of the second order Melnikov non-resonance conditions we develop a multiscale inductive approach 'a la Bourgain. A feature of the Monograph is to present the proofs, techniques and ideas developed in a self-contained and expanded manner." @default.
- W3008686246 created "2020-03-06" @default.
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- W3008686246 date "2020-10-09" @default.
- W3008686246 modified "2023-10-03" @default.
- W3008686246 title "Quasi-Periodic Solutions of Nonlinear Wave Equations on the $d$-Dimensional Torus" @default.
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- W3008686246 doi "https://doi.org/10.4171/211" @default.
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